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Question : The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°. The height (in metres) that the pillar raised so that its angle of elevation at the same point may be 45°, is:

Option 1: 63.4

Option 2: 86.6

Option 3: 126.8

Option 4: 173.2


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 8th Jan, 2024

Correct Answer: 63.4


Solution : Given: The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°.

In $\triangle DBC$, $\tan 30°=\frac{DB}{BC}$
$⇒\frac{1}{\sqrt3}=\frac{DB}{150}$
$⇒DB=\frac{150}{\sqrt3}$
$⇒DB=50\sqrt3$
In $\triangle ABC$, $\tan45°=\frac{AB}{BC}$
$⇒1=\frac{AB}{150}$
$⇒AB=150$ m
Also, $AD = AB - DB$
$⇒AD=150 - 50\sqrt3$
$⇒AD=150-50\times 1.732$
$⇒AD=150-86.6$
$\therefore AD=63.4$ m
Hence, the correct answer is 63.4.

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